Collaborative Research: Modeling Unobserved Heterogeneity in Network Formation

网络的统计分析在社会科学和行为科学中变得越来越重要，近年来已被应用于各种各样的问题。事实上，美国国家科学基金会的社会科学议程设定声明，“重建马赛克”，承认网络科学是四个关键的研究前沿之一。然而，尽管对网络的统计分析不断受到学者和广大公众的广泛关注，但对网络的定量研究仍处于发展的早期阶段。直到最近才发展出统计理论和计算技术来严格分析各种类型的网络。该项目的中心目标是开发一种新模型，用于识别对网络形成的统计影响，明确说明未观察到的变化。技术概述pi开发了一种估计器，可以准确捕获网络模型中地层中未观察到的异质性。他们通过扩展广泛应用的指数随机图模型（ERGM）来实现这一目标，其中包括一个脆弱项，用于解释未测量、未观察或无法想象的异质性。未解释的异质性是社会过程研究中的一个重要问题；因此，无法有效地对其进行建模是一个重要的差距，限制了ergm在许多潜在兴趣领域的适用性。事实上，ERGM的两个主要假设之一是模型是正确指定的，违反这一假设可能导致系数偏差或模型简并。pi建议扩展ERGM，通过引入脆弱项来解释这个问题，从而创建一个脆弱指数随机图模型（FERGM）。除了定义FERGM并提供蒙特卡罗模拟来证明该方法的模型特性和比较效益外，pi还将FERGM应用于社会和健康科学的实质性主题，并为其他人提供相关的统计软件。网络建模的进步将在包括社会学、经济学、统计学、计算机科学和行为健康在内的科学学科中发挥作用。对社会科学应用的关注将有助于公共政策的实践者，使他们能够更准确地评估政策对经济和社会结果的重要性。最后，该项目直接促进了教学、培训和学习，并扩大了代表性不足群体在学术活动中的参与。

General SummaryThe statistical analysis of networks has become increasingly important in the social and behavioral sciences and has been applied to a diverse range of problems in recent years. Indeed, the National Science Foundation's agenda setting statement for the social sciences, "Rebuilding the Mosaic," recognizes Network Science as one of four critical research frontiers. Yet, while the statistical analysis of networks continues to attract a great deal of attention from scholars and the broader public, the quantitative study of networks remains in the early stages of development. Only recently have the statistical theory and computational techniques been developed to rigorously analyze various types of networks. The central aim of the project is to develop a new model for identifying statistical effects on network formation that explicitly accounts for unobserved variation. Technical SummaryThe PIs develop an estimator that accurately captures unobserved heterogeneity in tie formation in network models. They do so by extending the widely applied Exponential Random Graph Model (ERGM) to include a frailty term that accounts for unmeasured, unobserved, or unimagined heterogeneity. Unaccounted heterogeneity is a significant issue in the study of social processes; thus, the inability to effectively model it is an important gap that limits the applicability of ERGMs in many areas of potential interest. In fact, one of the two major assumptions of the ERGM is that the model is correctly specified, and coefficient bias or model degeneracy may result from violations of this assumption. The PIs propose to extend the ERGM to account for this problem through the introduction of a frailty term, thereby creating a Frailty Exponential Random Graph Model (FERGM). In addition to defining the FERGM and providing Monte Carlo simulations to demonstrate the model properties and comparative benefits of the approach, the PIs apply the FERGM to substantive topics in the social and health sciences and provide related statistical software for others to do so as well. Advances in network modeling will be useful across scientific disciplines, including sociology, economics, statistics, computer science and behavioral health. The focus on social science applications will aid practitioners in public policy by allowing them to more accurately evaluate the importance of policy on economic and social outcomes. Finally, the project directly promotes teaching, training, and learning and broadens participation of underrepresented groups in scholarly activity.